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Lipschitz representations of subsets of the cube

Mendelson, Shahar


We show that for any class of uniformly bounded functions H with a reasonable combinatorial dimension, the vast majority of small subsets of the n-dimensional combinatorial cube cannot be represented as a Lipschitz image of a subset of H, unless the Lipschitz constant is very large. We apply this result to the case when H consists of linear functionals of norm at most one on a Hilbert space.

CollectionsANU Research Publications
Date published: 2007-11-14
Type: Journal article
Source: Proceedings of the American Mathematical Society
DOI: 10.1090/S0002-9939-06-08620-5


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